Question

How would the expression x^3-8 be written using difference of cubes

Answer 1

we can use formula

$a^3-b^3=(a-b)(a^2+ab+b^2)$

we can compare

we get

a=x

b=2

now, we can plug that in formula

and we get

$x^3-2^3=(x-2)(x^2+2x+2^2)$

now, we can simplify it

$x^3-8=(x-2)(x^2+2x+4)$...........Answer

Answer 2

$a^3 - b^3 = (a - b)(a^2 + ab + b^2)$

$x^3 - 8 =$

$= x^3 - 2^3$

$= (x - 2)(x^2 + x(2) + 2^2)$

$= (x - 2)(x^2 + 2x + 4)$

Answer: (x - 2)(x^2 + 2x + 4)